On the validity of the von Neumann-Mullins relation
On the validity of the von Neumann-Mullins relation
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论冯·诺依曼-马林斯关系的有效性
DOI：
10.1016/j.scriptamat.2004.05.023
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发表时间：
2004
影响因子：
6
通讯作者：
L. Shvindlerman
中科院分区：
文献类型：
--
作者：
G. Gottstein;A. Rollett;L. Shvindlerman
基于经典的von Neumann-Mullins （VN-M）分析，我们提出了二维网络中晶粒相对生长或收缩速率的新分析。我们发现，对晶粒形状在收缩或生长过程中的稳定性分析表明，规则的二维晶粒的任何变化都会导致形状的变化。我们还重新检查了最近的一项分析，该分析声称VN-M关系无效，但发现它仍然有效，并且引用的分析实际上混淆了二阶修正和一阶问题，部分原因是它们的推导是错误的。错误的差异大小导致他们用非物理问题来解释这种差异。曲率沿晶粒周长分布的方式只能引起作为晶粒拓扑（边数）函数的面积变化率的二阶修正。
We present a new analysis of the relative rate of growth or shrinkage of grains in a two-dimensional network, based on the classical von Neumann–Mullins (VN–M) analysis. We find that an analysis of the stability of the grain shape during shrinkage or growth shows that any change in the regular 2D grain leads to changes in the shape. We also re-examine a recent analysis that claims to have invalidated the VN–M relationship, but find that it is still valid, and that the cited analysis, in fact, confused a second order correction with a first order problem, partly because their derivation was in error. The erroneous magnitude of the discrepancy led them to use unphysical issues to explain the discrepancy. The way in which the curvature is distributed along the perimeter of a grain only gives rise only to second order corrections to the rate of change of area as a function of grain topology (number of sides).